Papers

We propose a nonlocal extension of the generalized Dirac oscillator (GDO) in $(1+1)$ dimensions by replacing the multiplicative interaction $f(x)$ with an integral operator $\hat F$ with kernel $f(x,x')$. The resulting Dirac equation preserves an operator factorization and decouples into two nonlocal Schrödinger-type (Sturm–Liouville) equations for the spinor components. We derive explicit expressions for the associated supersymmetric partner kernels in terms of $f$ and its derivatives, and we show that a complex-translation metric $\eta=e^{-\theta p_x}$ leads to a simple sufficient kernel-level pseudo-Hermiticity constraint, $f(x+\ii\hbar\theta,x'+\ii\hbar\theta)=f^*(x',x)$, extending the familiar local complex-shift criteria. To provide a transparent nonlocal-to-local interpretation, we adapt the Coz–Arnold–MacKellar current-based localization to each component equation, obtaining energy-dependent equivalent local potentials and multiplicative Perey (damping) factors. The mapping breaks down precisely at current zeros, thereby diagnosing the spurious solutions of the corresponding nonlocal Schrödinger problem. Finally, we illustrate the formalism with analytically tractable benchmarks (the local Dirac oscillator and a translation-invariant kernel) and with a finite-rank separable model (Gaussian form factor) that reduces the integro-differential problem to a small set of coupled ordinary differential equations and algebraic constraints.

Increasingly deeper integration of HPC resources and QPUs unveils new challenges in computer architecture and engineering. As a consequence, dependability arises again as a concern encompassing resilience, reproducibility and security. The properties of quantum computing systems involve a reinterpretation of these factors in retrodictive, predictive, and prescriptive ways. We state here that resilience must become an a priori design constraint rather than an afterthought of HPC-QPU integration. This article describes the need for conceptual and quantitative models to estimate and assess the resilience hybrid classical-quantum computing infrastructure. We suggest how resilience methods in civil engineering can apply at various levels of the classical-quantum computing stack. We also discuss implications of a model of end-user value for the estimation of consequences resulting from the propagation of vulnerabilities from a given level of the stack upwards. Finally, we argue in favor of new resilience models can help the impact of improving specific components in quantum technology stacks to provide a clearer picture about the value of separation of concerns across different layers. Ultimately, HPC-QPU integration will increasingly demand more precise statements about the cost-benefit ratio of specific system improvements and their cascading consequences against estimates of delivered value to users.

The Variational Quantum Algorithms (VQAs) are hybrid quantum-classical algorithms and they can be used in the Nosiy Intermadiate Scale Quantum (NISQ) devises. The Variational Quantum Eigensolver (VQE) was suggested as a first VQA. VQE is based on the variational method of quantum mechanics and it is used to find the ground state energy of a quantum system. In this study, VQE is used for the analysis of NMR spectra for the AB and AB2 spin systems. The frequencies and the spin coupling values are obtained from the sample spectra for these spin systems. Then the Hamiltonians are written in terms of pauli spin operators and transformed into a suitable forms for quantum computer. By employing VQE the ground state energies are obtained for the related spin systems. They are found to be in good agreement with the results obtained from the known variation method.

A unified framework is developed for determining whether a gravitational-wave (GW) background behaves as a classical field or as a genuinely quantum environment. Unified here means that both descriptions originate from the same tidal coupling derived from geodesic deviation, which yields an identical quadratic interaction Hamiltonian for the detector; the only distinction lies in whether the GW degrees of freedom are modeled as classical phase-randomized coherent states or as quantized graviton modes. Within this common framework, the reduced dynamics of a quantum harmonic oscillator exhibit a sharp structural contrast: a quantized graviton bath preserves coherence within the lowest phonon-number manifold, forming a protected sector at leading order, whereas a classical stochastic GW field inevitably induces decoherence even inside this subspace. This difference provides an operational criterion for diagnosing the classical or quantum nature of gravitational waves using mesoscopic optomechanical systems. Our results establish decoherence structure - not merely its magnitude - as a sensitive probe of gravitational quantumness and delineate the experimental regimes under which such tests may become feasible.

We investigate the impact of an isotropic antiferromagnetic Heisenberg perturbation on the toric code, focusing on the resulting quantum phase transition and the nature of the phase that emerges beyond topological order. Using neural-network quantum states (NQS), we compute ground states over a wide range of Heisenberg couplings while fully respecting the exact symmetries of the model. In the weak-coupling regime, the numerical results are in excellent agreement with an effective low-energy description derived from a Schrieffer-Wolff (SW) transformation, providing analytic control over the perturbative breakdown of topological order. We show that the Heisenberg perturbation only renormalizes local operators at low orders, whereas mixing between topological sectors occurs only at a perturbative order proportional to the system size. At intermediate values of the Heisenberg interaction, the topological phase breaks down. We estimate the critical point through a combination of the fidelity susceptibility and the logarithmic susceptibility of non-contractible Wilson loops for various system sizes. Furthermore, we utilize the topological entanglement entropy to provide a comprehensive characterization of the phase transition. Beyond the transition, an antiferromagnetic $\pm X/\pm Z$ Néel phase emerges, characterized by a fourfold-degenerate symmetry-broken manifold, which is explicitly probed using staggered-magnetization-based diagnostics. Our results show how local two-spin interactions, which naturally arise in realistic implementations of the toric code, drive the breakdown of topological order. Moreover, we establish the SW approach as a systematic framework for analyzing such perturbations in combination with variational many-body methods.

We propose a simple scalable scheme for the dissipative generation of entangled states of multiple emitters coupled to a waveguide. Our approach exploits collective interactions arising from the formation of subradiant and superradiant excited states, combined with the quantum Zeno effect. We show that, starting from an arbitrary initial state, the system deterministically evolves toward a W-type entangled steady state, with an infidelity that scales inversely with the cooperativity. The protocol is scalable to an arbitrary number of emitters. We further analyze the impact of additional experimental imperfections and present a detailed implementation based on trapped $^{133}$Cs atoms.

We exhibit a functor from the category OUS of order unit spaces and positive, unit-preserving mappings into the category $\Prob$ of probabilistic models (test spaces with designated state spaces) and morphisms thereof. Restricted to any subcategory of OUS monoidal with respect to a positive, normalized, bilinear composition rule, our functor is also monoidal. This shows that the convex-operational approach to physical theories can be subsumed by the test-space approach, without resort to “generalized test spaces”. A second construction, equipping a probabilistic model with tests representing “weighted coins”, also sheds light on the nature of unsharp observables.

Fermionic Gaussian states (FGSs) and the associated matchgate circuits play a central role in quantum information theory and condensed matter physics. Despite being possibly highly entangled, they can still be efficiently simulated on classical computers. We address the question of how to optimally create such states when using matchgate circuits acting on product states. To this end, we derive lower bounds on the number of gates required to prepare an arbitrary pure FGS: We establish both an asymptotic bound on the minimal gate count over general nearest-neighbor gate sets and an exact bound for circuits composed solely of matchgates. We present explicit algorithms whose constructions saturate these bounds, thereby proving their optimality. We furthermore determine when an FGS can be prepared with a circuit of any given depth, and derive an algorithm that constructs such a circuit whenever this condition is satisfied, either exactly or approximately. Our results have direct applications to (approximate) state preparation and to disentangling procedures. Moreover, we introduce a new classical simulation algorithm for matchgate circuits, based entirely on manipulating the generating circuits of the FGSs. Finally, we briefly study an extension of our framework for $t$-doped Gaussian states and circuits.

Local-operator entanglement (LOE) quantifies the nonlocal structure of Heisenberg operators and serves as a diagnostic of many-body chaos. We provide rigorous bounds showing when an operator can be well-approximated by a matrix-product operator (MPO), given asymptotic scaling of its LOE $\alpha$-Rényi entropies. Specifically, we prove that a volume law scaling for $\alpha\geq 1$ implies that the operator cannot be approximated efficiently as an MPO while faithfully reproducing all expectation values. On the other hand, if we restrict to correlations over a relevant sub-class of (ensembles of) states, then logarithmic scaling of the $\alpha < 1$ entropies implies MPO simulability. This result covers a range of relevant quantities, including infinite temperature autocorrelation functions, out-of-time-ordered correlators, and average-case expectation values over ensembles of computational basis states. Beyond this regime, we provide numerical evidence together with a random matrix model to argue that this simulability result also typically holds for arbitrary states. Our results put on firm footing the heuristic expectation that a low operator entanglement implies efficient tensor network representability, extending celebrated foundational results from the theory of matrix-product states and providing a formal link between quantum chaos and classical simulability.

Magnetic spectroscopy at the nanoscale provides unique insights into material properties and dynamics, with quantum sensors like nitrogen-vacancy (NV) centers being ideally suited for these scales. However, detecting low-frequency signals remains a challenge due to finite coherence times ($T_2^*$), as signals oscillating slower than $1/T_2^*$ decay before sufficient phase accumulation occurs. We present RESOLUTE (Ramsey corrElation SpectroscOpy puLse seqUence wiTh phasE cycling), a protocol that overcomes these limitations by combining Ramsey measurements with correlation spectroscopy. By storing accumulated phase as a population imbalance during a correlation period ($T_\mathrm{corr} < T_1$) between two sensing periods, RESOLUTE generates an effective coherence time $T_2^p > T_2^*$. This shifts the frequency-matching condition to the correlation time, enabling detection in the previously inaccessible spectral region between $1/T_1$ and $1/T_2^p$. We experimentally demonstrate an extension of the effective coherence time from $T_2^* = 0.38\,\mu s$ to $T_2^p = 5.1\,\mu s$, surpassing Hahn Echo measurements. The technique successfully detects $^{13}$C nuclear spin Larmor precession at fields as low as 49$\,$G ($\sim$50$\,$kHz). We further provide theoretical insight using Fisher information to characterize RESOLUTE's frequency estimation capabilities compared to existing protocols. Finally, by integrating adiabatic pulses and phase cycling, we demonstrate robust spin control and effective DC signal extraction. These advancements provide enhanced sensitivity to weak dipolar interactions, essential for single-molecule imaging and quantum sensing applications.

Continuous-time quantum walks (CTQWs) exhibit localization phenomena that differ fundamentally from their classical counterparts, yet the precise relationship between network structure, spectral degeneracy, and confined dynamics remains incompletely understood. In this work, we present a complete analytical characterization of localization in CTQWs on two highly symmetric graph families: barbell graphs and star-of-cliques graphs. These networks combine pronounced spectral degeneracy with modular structure, enabling exact diagonalization and explicit computation of both eigenstate and dynamical inverse participation ratios (IPRs). Our analysis reveals that localization is governed by the interplay between degenerate subspaces, which generate families of confined modes, and hybridization between invariant subspaces, which redistributes spectral weight. Notably, the dynamical IPR can exceed expectations based solely on eigenstate IPRs, demonstrating that coherent superposition within degenerate eigenspaces enhances confinement. By connecting IPR values to the effective number of vertices visited, we provide a structural diagnostic for predicting quantum transport outcomes in modular networks, establishing that connectivity alone can determine where and how strongly a quantum walk localizes.

A quantum wavemetry scheme based on the coherence de Broglie wavelength (CBW) is proposed using an M coupled Mach Zehnder interferometer (MZI) architecture to achieve superresolution sensing and metrology. Although CBW does not attain the Heisenberg limit, it circumvents the key practical limitations of N00N state based quantum sensing, including restricted photon number N, reduced fringe visibility, and strong susceptibility to photon loss. The CBW approach enables loss tolerant operation with arbitrarily large M, while maintaining near unity fringe visibility. Fully compatible with coherence optics, the CBW scheme can be directly integrated into conventional wavemetry systems, providing both superresolution and enhanced sensitivity. A proof of principle experiment demonstrating CBW based superresolution is implemented using a Sagnac integrated round trip MZI structure for M=2, validating the feasibility of the proposed quantum wavemetry design.

We introduce a notion of the “explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard pullback construction (notwithstanding that $\Prob$ does not support arbitrary pullbacks). We then show that every locally-finite probabilistic model has a canonical, sharp classical explanation. The construction is functorial, so every locally-finite probabilistic theory has a canonical, sharp classical (though of course, usually non-local) representation.

The quantum simulation of topological phases in (2+1)D quantum electrodynamics with Wilson fermions provides a promising route toward realizing topological phenomena in near-term lattice experiments. We show that the commonly used staggered-fermion discretizations in Hamiltonian gauge theories possesses an exact time-reversal symmetry, which forbids the emergence of nontrivial topological phases and has led to confusion in the existing literature. In this work, we resolve this obstacle by systematically analyzing fermion discretization effects in (2+1)D lattice Hamiltonians of fermions coupled to U(1) gauge fields that satisfy Gauss' law. We show that Wilson fermions, already in the minimal one-flavor theory, naturally enable topological regimes with nonzero Chern numbers, and that the two-flavor extension at finite chemical potential further enriches the accessible topological structure. We develop gauge-invariant diagnostics of topological response, including many-body Chern numbers and current correlators that remain robust probes at weak coupling. Finally, through extensive exact diagonalization calculations across both flavor settings, we characterize the spectrum, correlators, and topological invariants, providing a concrete foundation for near-term quantum simulations of topological phases in lattice field theories. The implications of this work for quantum simulations of lattice field theory are analyzed in a joint submission [1].

Donor impurities in wide direct band gap semiconductors provide a promising platform for spin–photon quantum technologies by combining a donor spin qubit with optically addressable transitions. In ZnO, the shallow donor with the largest reported binding energy has long been associated with the I$_{10}$ bound exciton line, but its microscopic origin has remained unresolved. Here we demonstrate the controlled formation and identification of this donor as a Sn–Li complex through a combination of ion implantation, annealing, optical spectroscopy, and first-principles calculations. Resonant two-laser coherent population trapping measurements reveal an electron–$^{119}$Sn hyperfine interaction of $392 \pm 15$\,MHz, establishing a coupled electron–spin–1/2, nuclear–spin–1/2 system with one of the largest hyperfine couplings reported for shallow donors in semiconductors. Density functional theory calculations show that a nearest-neighbor Sn$_{\mathrm{Zn}}$–Li$_{\mathrm{Zn}}$ complex has favorable formation energetics, donor character with the electron localized on Sn, and an extrapolated hyperfine interaction consistent with experiment. The large donor binding energy and excited-state structure indicate enhanced thermal robustness of the optical transition relative to conventional group–III donors, while the strong hyperfine interaction enables fast electron–nuclear spin control and prospects for direct nuclear–spin–photon interfaces. We further observe efficient optically induced nuclear spin polarization, highlighting a path toward nuclear spin initialization. More broadly, our results reveal how a donor–acceptor complex can access previously unexplored regimes of shallow donor physics, extending the design space of quantum defects beyond isolated substitutional dopants.

Tunnel-coupled optically active quantum dot molecules (QDMs), have the potential to operate as spin-photon-interfaces with coupled spins that interact with two different photon frequencies at the same time. A prerequisite is to deterministically prepare two (electron or hole) spins in the QDM and be able to electrically tune the orbital state couplings. Here, we demonstrate the sequential optical charging of a single QDM with two electron spins while simultaneously maintaining the ability to widely tune orbital couplings using static electric fields and optically drive the system for quantum light generation. We optically prepare one- and two-spin states, initialize via optical pumping and explore orbital and spin relaxation dynamics for one and two-spin states as a function of the energy detuning and hybridization of orbital states. For two-spin states, remarkably long S-T relaxation times are observed extending beyond $\sim 100\mu s$ with strong dependence on the relative energy of ground and excited two-spin states. Qualitative agreement is observed with $\mathbf{k \cdot p}$ calculations of phonon-mediated spin-relaxation. Our results provide new quantitative understanding of the dynamics of one and two-spin states and confirm their suitability of QDMs for creating multidimensional photonic cluster states by exploiting tunable spin-spin exchange couplings at zero magnetic fields combined with optical driving.

We investigate a two-dimensional matter-wave interferometer where both spatial and rotational dynamics of a nanoparticle are intertwined in closing the one-loop interferometer in the Stern-Gerlach type setup. We consider the spin-contrast of the nitrogen-vacancy (NV) centred nanodiamond in combination with a two-dimensional magnetic field setup to extend the one-dimensional Stern–Gerlach interferometry. We analyse the dynamical motion along with the rigid rotation under the influence of the external magnetic field. Regarding rotation, we incorporate Euler-angle dynamics to analyse the stability of rotational degrees of freedom and their influence on the spin contrast to address the Humpty-Dumpty problem. We show that by imparting external rotation provides the gyroscopic stability to the liberating mode of the NV-spin and hence helps to improve the contrast. Our scheme creates a tiny spatial superposition of size $\sim 0.21~{\rm \mu m}$ for mass $m=10^{-17}$kg in less than $t\sim 0.013$s.

Multimode cavity-QED systems can be leveraged to explore a wide range of physical phenomena; however, a complex multimode environment makes systematic characterization of light-matter interactions challenging. Here we present a general measurement protocol, applicable to both atomic and synthetic cavity-QED systems, that enables the determination of coupling to individual photonic modes. The method leverages measurements of the AC-Stark and Kerr effects, along with known detuning dependencies, to eliminate the need for single-photon resolution, independent photon-number calibration, or insertion-loss calibration. We demonstrate the method using a superconducting transmon qubit coupled to a one-dimensional microwave resonator lattice. We validate the consistency of the extracted light-matter couplings $g$ determined at multiple qubit detunings, and from the self-Kerr and cross-Kerr shifts for three photon modes, which provide separate measurements of $g$ for each of the three modes.

We find the dispersion relations of two elusive families of core-bound excitations of the Gross-Pitaevskii (GP) vortex, varicose (axisymmetric) and fluting (quadrupole) waves. For wavelengths of order the healing length, these two families – and the well-known Kelvin wave – possess an infinite sequence of core-bound, vortex-specific branches whose energies lie below the Bogoliubov dispersion relation. In the short-wavelength limit, these excitations can be interpreted as particles radially bound to the vortex, which acts as a waveguide. In the long-wavelength limit, the fluting waves unbind from the core, the varicose waves reduce to phonons propagating along the vortex, and the fundamental Kelvin wave is the only core-bound vortex-specific excitation. Finally, we propose a realistic spectroscopic protocol for creating and detecting the varicose wave, which we test by direct numerical simulations of the GP equation.

We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be leveraged to perform non-Clifford gates in $\mathbb{Z}_2$ surface codes, thus enabling universal computation along with established means of performing logical Clifford gates. Moreover, for suitably chosen groups, we demonstrate that arbitrary reversible classical gates can be implemented transversally in the group surface code. We present the logical operations in terms of a set of elementary logical operations, which include transversal logical gates, a means of transferring encoded information into and out of group surface codes, and preparation and readout. By composing these elementary operations, we implement a wide variety of logical gates and provide a unified perspective on recent constructions in the literature for sliding group surface codes and preparing magic states. We furthermore use tensor networks inspired by ZX-calculus to construct spacetime implementations of the elementary operations. This spacetime perspective also allows us to establish explicit correspondences with topological gauge theories. Our work extends recent efforts in performing universal quantum computation in topological orders without the braiding of anyons, and shows how certain group surface codes allow us to bypass the restrictions set by the Bravyi-König theorem, which limits the computational power of topological Pauli stabilizer models.

Continuous-variable quantum systems are central to quantum technologies, with Gaussian states playing a key role due to their broad applicability and simple description via first and second moments. Distinguishing Gaussian states requires computing their trace distance, but no analytical formula exists for general states, and numerical evaluation is difficult due to the exponential cost of representing infinite-dimensional operators. We introduce an efficient numerical method to compute the trace distance between a pure and a mixed Gaussian state, based on a generalized Lanczos algorithm that avoids explicit matrix representations and uses only moment information. The technique extends to non-Gaussian states expressible as linear combinations of Gaussian states. We also show how it can yield lower bounds on the trace distance between mixed Gaussian states, offering a practical tool for state certification and learning in continuous-variable quantum systems.

The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's fault tolerance and overhead, the decoder's quality, and the device's constraints, such as physical qubit count and connectivity. This work makes two contributions towards error-corrected quantum devices. First, we introduce mirror codes, a simple yet flexible construction of LDPC stabilizer codes parameterized by a group $G$ and two subsets of $G$ whose total size bounds the check weight. These codes contain all abelian two-block group algebra codes, such as bivariate bicycle (BB) codes. At the same time, they are manifestly not CSS in general, thus deviating substantially from most prior constructions. Fixing a check weight of 6, we find $[[ 60, 4, 10 ]], [[ 36, 6, 6 ]], [[ 48, 8, 6 ]]$, and $[[ 85, 8, 9 ]]$ codes, all of which are not CSS; we also find several weight-7 codes with $kd > n$. Next, we construct syndrome extraction circuits that trade overhead for provable fault tolerance. These circuits use 1-2, 3, and 6 ancillae per check, and respectively are partially fault-tolerant (FT), provably FT on weight-6 CSS codes, and provably FT on all weight-6 stabilizer codes. Using our constructions, we perform end-to-end quantum memory experiments on several representative mirror codes under circuit-level noise. We achieve an error pseudothreshold on the order of $0.2\%$, approximately matching that of the $[[ 144, 12, 12 ]]$ BB code under the same model. These findings position mirror codes as a versatile candidate for fault-tolerant quantum memory, especially on smaller-scale devices in the near term.

Characterizing the dynamics of open quantum systems at the level of microscopic interactions and error mechanisms is essential for calibrating quantum hardware, designing robust simulation protocols, and developing tailored error-correction methods. Under Markovian noise/dissipation, a natural characterization approach is to identify the full Lindbladian generator that gives rise to both coherent (Hamiltonian) and dissipative dynamics. Prior protocols for learning Lindbladians from dynamical data assumed pre-specified interaction structure, which can be restrictive when the relevant noise channels or control imperfections are not known in advance. In this paper, we present a sample-efficient protocol for learning sparse Lindbladians without assuming any a priori structure. Our protocol is ancilla-free, uses only product-state preparations and Pauli-basis measurements, admits provably stable coefficient reconstruction, and achieves near-optimal time resolution, making it compatible with near-term experimental capabilities. Together, this provides a systematic route to scalable characterization of open-system quantum dynamics, especially in settings where the error mechanisms of interest are unknown.

We study the decoding problem for quantum Tanner codes and propose to exploit the underlying local code structure by grouping check nodes into more powerful generalized check nodes for enhanced iterative belief propagation (BP) decoding by decoding the generalized checks using a maximum a posteriori (MAP) decoder as part of the check node processing of each decoding iteration. We mainly study the finite-length setting and show that the proposed enhanced generalized BP decoder for quantum Tanner codes significantly outperforms the standard quaternary BP decoder with memory effects, as well as the recently proposed Relay-BP decoder, even outperforming generalized bicycle (GB) codes with comparable parameters in some cases. For other classes of quantum low-density parity-check (qLDPC) codes, we propose a greedy algorithm to combine checks for generalized BP decoding. However, for GB codes, bivariate bicycle codes, hypergraph product codes, and lifted-product codes, there seems to be limited gain by combining simple checks into more powerful ones. To back up our findings, we also provide a theoretical cycle analysis for the considered qLDPC codes. This leads us to a construction criterion for quantum Tanner codes that produces codes particularly well-suited for BP decoding.

We present a fast and effective framework for analysing and designing syndrome extraction circuits (SECs). Our approach is based on left–right circuits, a general SEC design that maintains low depth and avoids gate interleaving constraints by staggering $X$ and $Z$ stabiliser checks. Initially proposed for specific classes of codes, we generalise this construction to arbitrary CSS codes and optimise the circuit structure to achieve low qubit idling time, large effective distance, and reduced minimum-weight failure mechanisms. A key component of our framework is the formal notion of residual errors and their associated distance metrics, which form lightweight proxies for capturing error propagation and quantifying the potential harm of circuit-level errors. Applying our automated framework to diverse classes of codes, we observe consistent improvements in logical performance of up to an order of magnitude compared to existing single-ancilla SEC designs. Moreover, by directly applying these proxies, we prove that no non-interleaving SEC can achieve circuit distance $12$ for the gross code, and we identify an explicit circuit that we conjecture achieves distance $11$, exceeding previously known constructions.

We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge the gap between theory and implementation by developing and comparing three concrete realizations of the algorithm. First, we implement a sparse initial state preparation combined with product-formula (Suzuki-Trotter) Hamiltonian simulation. Second, we implement a fully quantum, oracle-based framework in which classical data are accessed via oracles, the Hamiltonian is block-encoded, and time evolution is performed using QSVT-based Hamiltonian simulation. Third, we propose an efficient alternative that combines the sparse state-preparation routine of the first approach with the oracle and block-encoding-based simulation pipeline of the second. We provide these implementations on Classiq, a high-level quantum design platform and provide appropriate resource benchmarks. Our simulation results show that the complex initial state preparation proposed by Babbush et al. can be circumvented at least in the linear-chain case. Finally, we illustrate two physical applications-extracting normal modes and simulating coarse-grained energy propagation-demonstrating how the algorithm connects to measurable observables. Our results clarify the resource requirements of the algorithm and provide concrete pathways toward practical quantum advantage.

Quantum-gas microscopes provide direct access to the phases of the Hubbard model, bringing microscopic insight into the complex competition between interactions, SU(2) magnetism, and doping. Alkaline-earth(-like) fermions extend this spin-1/2 paradigm by realizing higher symmetries and giving access to SU($N$) Hubbard models, with rich phase diagrams to be unveiled. Despite its fundamental interest, a microscopic exploration of SU($N$) quantum systems has remained elusive. Here we report the realization of a quantum-gas microscope for fermionic $^{87}$Sr. Our imaging scheme, based on cooling and fluorescence on the narrow intercombination line at 689 nm, enables spin-resolved single-atom detection. By implementing a spin-selective optical pumping protocol, we determine the occupation of each of the 10 spin states in a single experimental realization, a crucial capability for probing site-resolved magnetic correlations. We benchmark our method by observing single-particle Larmor precession across the full spin-9/2 ground-state manifold and use numerical simulations of SU($N$) Fermi-Hubbard chains, incorporating the measured detection fidelities, to demonstrate its capability to resolve many-body spin correlations. Our results establish $^{87}$Sr quantum-gas microscopy as a powerful approach to study exotic magnetism in the SU($N$) Fermi-Hubbard model, and provide a new detection tool for studies in quantum simulation, computation, and metrology.

Amplitude estimation, in its original form, is formulated as phase estimation upon the Grover iterate. Subsequent improvements to the algorithm have eliminated the need for phase estimation and introduced low-depth variants that trade speedups for lower circuit depth. We make the key observation that amplitude estimation is equivalent to estimating the energy gap of an effective Hamiltonian, whereby discrete-time evolution is generated by amplitude amplification. This enables us to develop an amplitude estimation algorithm for both Heisenberg-limited and low-depth circuit regimes, inspired by statistical phase estimation techniques developed for early fault-tolerant ground-state energy estimation. In the Heisenberg-limited regime, our approach achieves performance comparable to state-of-the-art methods while using simplified classical post-processing. In the low-depth regime, it obtains optimal query–depth tradeoffs up to polylogarithmic factors, with provable guarantees and improved empirical performance over prior approaches. The resulting protocol is ancilla-free and requires only standard Grover reflections. Due to its flexibility, generality, and robustness, we expect our approach to be a key enabler for a broad range of early fault-tolerant applications.

Correlated noise is a critical failure mode in quantum error correction (QEC), yet a gap remains between the stochastic Pauli models used for scalable QEC analyses and the microscopic, non-Markovian descriptions of noise in physical devices. We bridge this gap by introducing Spatiotemporal Pauli Processes (SPPs): the natural multi-time generalization of Pauli channels, joint probability distributions over Pauli faults across space and time, obtained exactly from any noise process, however non-Markovian, under standard Pauli-frame randomization. SPPs thereby provide a single language in which correlated noise can be recast, compared, and extended, compatible with both microscopic open systems modeling and the stabilizer workflow of QEC design and analysis. Our central result is constructive: the multi-time Pauli twirl acts by local contractions on a process tensor network, yielding an explicit classical tensor network whose virtual bonds encode memory, bounded by the environment's Liouville-space dimension. Transfer operator diagnostics link memory spectra to correlation decay, and hidden Markov representations enable efficient sampling of correlated Pauli fault trajectories, mapping microscopically derived noise directly into circuit-level QEC simulation. We demonstrate this with surface code memory and stability benchmarks up to distance $19$. A temporal "storm" model with tunable correlation time shows that memory alone, at strictly fixed marginal error rates, systematically erodes the exponential error suppression expected from code distance. A genuinely spatiotemporal quantum cellular automaton bath maps exactly, under system twirling, to a nonlinear probabilistic cellular automaton; tuning its coherent interactions drives the noise into a pseudo-critical regime with critical slowing down and macroscopic error avalanches that reverse surface code distance scaling.

An algorithm for the generation of shuttling sequences is necessary for the operation of a linear segmented ion-trap quantum computer. The present work provides an implementation of an algorithm that produces sequences proved to be optimal for circuits with a quantum Fourier transform-like structure. Such optimality was proved in previous work of our group. We first present an approach for qubit mapping, i.e. determining the initial ordering of the ions, termed the common ion order, and develop a heuristic algorithm for its implementation. We explain how this heuristic is integrated in the shuttling sequence generation algorithm described in the previous work. The results show the increased performance of the heuristic in terms of reducing the number of required shuttling operations. The number of ion displacements required exhibits a polynomial increase in terms of the number of qubits, such that these operations become the main contribution to the overall resource cost. Furthermore, we show that multiple zones for gate interactions can reduce the amount of qubit register reordering.